Question

to find how high school students feel about hot lunches, adam walks to the nearest high school and gives a survey postcard to every twentieth student that enters the building. he asks the students to mail the postcard in if they choose to participate in the study.

why might the method used be biased?

□ asking every twentieth student does not accurately represent the student population.
□ it is likely that student opinions in one particular high school do not accurately represent the opinions of all high school students.
□ students that take the time to complete the survey and mail it in probably feel strongly about hot lunches.

done

Explanation:

• For the first option: Systematic sampling (asking every twentieth student) can be a valid sampling method and can represent the population if the list is random, so this is not a reason for bias here.
• For the second option: The problem is about bias in the method used (voluntary response and sampling from one school), but the main bias from the method (voluntary response) is better captured by the third option. However, sampling from one school is also a limitation, but the question is about the method (how he is collecting data - voluntary response and sampling every 20th at one school). But the third option is about the voluntary response bias: students who take time to mail back likely have strong opinions, which is a type of self - selection bias. The second option is about sampling from one school (a sampling frame issue), but the method's bias (the way he is collecting data from that school) is the voluntary response. Let's analyze each:
• Option 1: Systematic sampling (nth student) is a valid technique and can be representative if the population is ordered randomly. So this is incorrect.
• Option 2: This is about the sampling frame (only one high school) not representing all high school students. But the question is about the method used (the way he is surveying within that school - giving postcards and asking to mail back). The bias from the method (not the sampling frame) is the voluntary response. However, if we consider the method as a whole (including sampling from one school), but the main bias in the data collection method (the way he gets responses) is self - selection. But let's re - evaluate: The method he used includes two parts: sampling every 20th student at one school and then a voluntary response (students choose to mail back). The third option is about the voluntary response: students who respond are likely those with strong feelings, which is a bias. The second option is about the sample not being representative of all high school students (sampling frame), but the question is "why might the method used be biased?". The method's bias (the way he collects data) is the voluntary response. So the third option is correct.
• Option 3: Since it's a voluntary response (students choose to participate by mailing back), those who do so are more likely to have strong opinions (either positive or negative) about hot lunches. This creates a self - selection bias, as the sample is not a random sample of all students (only those with strong feelings are likely to respond).

Answer:

C. Students that take the time to complete the survey and mail it in probably feel strongly about hot lunches. (assuming the options are labeled A, B, C in order as given: A. Asking every twentieth student...; B. It is likely that student opinions...; C. Students that take the time...)